@inbook{3224e350c1fc4bdfa80ca4a62ec3cc89,

title = "A family of unitary operators satisfying a poisson-type summation formula",

abstract = "We consider a weighted form of the Poisson summation formula. We prove that under certain decay rate conditions on the weights, there exists a unique unitary Fourier-Poisson operator which satisfies this formula. We next find the diagonal form of this operator, and prove that under weaker conditions on the weights, a unique unitary operator still exists which satisfies a Poisson summation formula in operator form. We also generalize the interplay between the Fourier transform and derivative to those Fourier-Poisson operators.",

author = "Dmitry Faifman",

year = "2012",

doi = "https://doi.org/10.1007/978-3-642-29849-3_11",

language = "الإنجليزيّة",

isbn = "9783642298486",

series = "Lecture Notes in Mathematics",

pages = "191--204",

booktitle = "Geometric Aspects of Functional Analysis",

}